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ST_IsleRoyaleWB_2018.pdf (page 20 of 25)

SimBio Virtual Labs" | Isle Royale

SimBio Virtual Labs" | Isle Royale

xtension Exercise: What's the Difference?

(A)

(B)

(C)

In Exercise 2 you conducted an experiment comparing health of moose with wolves absent to

health of moose with wolves present. You probably observed at least a small difference between the

Number of Moose

samples, but does that really indicate that moose have greater fat stores when wolves are present?

M

The difference could be related to wolves, but it could also have arisen simply by chance. You might

Amount of Fat Stores

have accidentally selected very healthy moose

one time and unhealthy moose the other. How can

you know whether the difference in means between two samples is real?

[2.1]

Which of the above graphs (A, B, or C) would make the most convincing argument that

The short answer is that you can't. But you can make a good guess using statistics. In fact, "inferential

the difference in fat stores is real, and not just due to chance?

statistics" were invented to allow us to better uncover the truth and answer these sorts of questions.

A. Fat stones increased significantly while wolves were present.

In this section, you will perform a simple statistical test, called a t-test, to decide whether or not

[ 2.2 ]

Explain your choice:

the wolves' presence had a significant effect on moose fat stores. If we were to be very thorough

and formal in our t-test lesson, we would include a lengthy discussion of such concepts as random

variables, sampling distributions, standard errors, and alpha levels. These are important, but to keep

this short, we will just focus on the core ideas underlying the t-test.

You start with a question: Is the mean moose fat stores different when wolves are present versus absent?

The null hypothesis is

is no real difference. Under the null hypothesis, the

If there is a lot of variability in the data sets you are comparing, you will more likely see a difference

difference in your samples arises from chance. The alternative hypothesis is that there is an effect of

in their means just by chance, supporting the null hypothesis. Only if the difference in means is large

wolves on moose fat stores. In order to know which hypothesis your samples support, we examine

compared to the amount of variability in the data do you suppose that the difference might be real. A

the difference in means relative to the variability you observed.

statistic called : formalizes this intuition - in fact, ? is calculated as a ratio of 'difference in means' to

amount of variability'. Here is its formula (with the 'p' and 'a' subscripts referring to moose energy

[1]

Look back at Exercise 2 where you measured the fat stores of adult moose with wolves absent and

with wolves present vs. absent):

present, and record those values here. Note that the subscript'p' represents samples with wolves

present, while'a' represents those with wolves absent.

difference in means

xp -Xa

variability in samples

SE

[ 1.1 ]

Mean fat stores of adult moose, wolves present ( .x ) :

In the formula above, the mean values of the two samples is given by x,and x . The variability

[ 1.2]

Mean fat stores of adult moose, wolves absent ( T. ) :_

of values within the sampled data sets is incorporated into the denominator, where 'SE' stands for

[ 13]

Calculate the difference in mean fat stores ( x, - x_):

the 'standard error of the sample-mean difference' (a fancy-sounding phrase for a simple concept

variability). Calculating this value is straightforward but requires a few steps if you are doing it 'by

(21

Look at the following three hypothetical graphs. Each graph shows two distributions of moose fat

stores, one with wolves present (lighter gray line) and one with wolves absent (darkerline). Note that

hand'; the formula is:

var.

in each graph, mean moose fat stores are represented by dashed vertical lines, and the difference

SE -

var

in means is the same for all three. However, the variation in fat stores is smaller in the distributions

on the left, and larger in those on the right

Here, var, and var, are the variances for each sample, a measure of the amount of variability in the

values. Finally, n, and n. are the number of samples in each data set. If you have never calculated

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